Asymmetric Spotty Patterns for the Gray–Scott Model in R2

In this paper, we rigorously prove the existence and stability of asymmetric spotty patterns for the Gray-Scott model in a bounded two-dimensional domain. We show that given any two positive integers k 1 , k 2 , there are asymmetric solutions with k 1 large spots (type A) and k 2 small spots (type B). We also give conditions for their location and calculate their heights. Most of these asymmetric solutions are shown to be unstable. However, in a narrow range of parameters, asymmetric solutions may be stable.

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